On the Buchstaber invariant of simple convex 3-polytopes

Abstract

In this paper the author gives a method of constructing characteristic matrices, and uses it to determine the Buchstaber invariants of all simple convex 3-polytopes, which imply that each simple convex 3-polytope admits a characteristic function. As a further application of the method, the author also gives a simple new proof of five-color theorem.

Keywords

Simple convex polytope / Characteristic function / Buchstaber invariant

References

[1] Buchstaber V M, Panov T E. Torus actions and their applications in topology and combinatorics, 2002, Providence, RI: Amer. Math. Soc.

[2] Davis M, Januszkiewicz T. Convex polytopes, Coxeter orbifolds and torus actions. Duke Math. J., 1991, 61: 417-451

[3] Erokhovets, N., Buchstaber invariant of simple, arXiv: 0908.3407.

[4] Fukukawa, Y. and Masuda, M., Buchstaber invariant of skeleta of a simplex, arXiv: 0908.3448.

[5] Grünbaum B. Convex polytopes. Bull. London Math. Soc., 1969, 1: 257-300

[6] Lü Z, Yu L. Topological types of 3-dimensional small covers. Forum Math., 2011, 23: 245-284